(A) For the quadratic equation $ax^2 + bx + c = 0$,the discriminant $D$ is given by $D = b^2 - 4ac$.Here,$a = 1$,$b = -\sqrt{13}$,and $c = 1$.$D = (-\

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(A) For the quadratic equation $ax^2 + bx + c = 0$,the discriminant $D$ is given by $D = b^2 - 4ac$.Here,$a = 1$,$b = -\sqrt{13}$,and $c = 1$.$D = (-\sqrt{13})^2 - 4(1)(1) = 13 - 4 = 9$.Since $D > 0$ and $D$ is a perfect square,the roots are real,distinct,and rational.However,since the coefficient $b = -\sqrt{13}$ is irrational,the roots are real and distinct.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

The roots of the equation $x^2 - \sqrt{13}x + 1 = 0$ are:

A
Real and distinct
B
Real and equal
C
Imaginary
D
Rational and different

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The roots of the equation $x^2 - \sqrt{13}x + 1 = 0$ are:

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